Questions: T is the midpoint of SU. Complete the proof that triangle STV is congruent to triangle UTW. Statement Reason --- --- 1 T is the midpoint of SU 2 UW is congruent to SV 3 TW is congruent to TV 4 ST is congruent to TU 5 triangle STV is congruent to triangle UTW

T is the midpoint of SU. Complete the proof that triangle STV is congruent to triangle UTW. Statement Reason --- --- 1 T is the midpoint of SU 2 UW is congruent to SV 3 TW is congruent to TV 4 ST is congruent to TU 5 triangle STV is congruent to triangle UTW
Transcript text: $T$ is the midpoint of $\overline{S U}$. Complete the proof that $\triangle S T V \cong \triangle U T W$. \begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & $T$ is the midpoint of $\overline{S U}$ & \\ \hline 2 & $\overline{U W} \cong \overline{S V}$ & \\ 3 & $\overline{T W} \cong \overline{T V}$ & \\ 4 & $\overline{S T} \cong \overline{T U}$ & \\ \hline 5 & $\triangle S T V \cong \triangle U T W$ & \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Given Information

We are given that T is the midpoint of $\overline{SU}$. We are also given that $\overline{UW} \cong \overline{SV}$ and $\overline{TW} \cong \overline{TV}$. We want to prove that $\triangle STV \cong \triangle UTW$.

Step 2: Definition of Midpoint

Since T is the midpoint of $\overline{SU}$, we know that $\overline{ST} \cong \overline{TU}$.

Step 3: Side-Side-Side (SSS) Congruence

We have $\overline{UW} \cong \overline{SV}$, $\overline{TW} \cong \overline{TV}$, and $\overline{ST} \cong \overline{TU}$. Therefore, by the SSS Congruence Postulate, $\triangle STV \cong \triangle UTW$.

Final Answer:

The proof is as follows:

| Statement | Reason | |---|---| | 1. T is the midpoint of $\overline{SU}$ | Given | | 2. $\overline{UW} \cong \overline{SV}$ | Given | | 3. $\overline{TW} \cong \overline{TV}$ | Given | | 4. $\overline{ST} \cong \overline{TU}$ | Definition of Midpoint | | 5. $\triangle STV \cong \triangle UTW$ | SSS Congruence Postulate |

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